Question

out of a ribbon of length 2 3/4 m, a piece of a length 1 1/3 m is used to make flowers
How much ribbon is left?

Answer 1

To find out how much ribbon is left after using a piece for making flowers, we need to subtract the length of the used piece from the original length of the ribbon.

The original length of the ribbon is \(2 \frac{3}{4}\) m, which can be converted to an improper fraction:

\[
2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ m}
\]

The piece of ribbon used is \(1 \frac{1}{3}\) m, which can also be converted to an improper fraction:

\[
1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \text{ m}
\]

Now, we will subtract the length of the used piece from the original length of the ribbon:

\[
\frac{11}{4} - \frac{4}{3}
\]

To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 3 is 12. We convert both fractions to have a denominator of 12.

\[
\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
\]
\[
\frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12}
\]

Now, we can perform the subtraction:

\[
\frac{33}{12} - \frac{16}{12} = \frac{33 - 16}{12} = \frac{17}{12}
\]

The result \( \frac{17}{12} \) m can be converted back to a mixed number:

\[
\frac{17}{12} = 1 \frac{5}{12} \text{ m}
\]

Therefore, the amount of ribbon left is \(1 \frac{5}{12}\) m.